Bianchi Type-II String Cosmological Model with Magnetic Field in f (R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of f(R,T) gravity proposed by Harko et al. (Phys Rev D 84:024020, 2011). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento B 74:182, 1983) cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=μ T. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Bianchi type-III Dark Energy Model in f(R,T) Gravity

A dark energy model with EoS parameter is investigated in f(R,T) gravity in Bianchi type-III space-time in the presence of perfect fluid source. To obtain a determinate solution special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B 74:183, 1983) is used. We have also assumed that the scalar expansion is proportional to shear and the EoS parameter is proportional to skewness parameter. It is observed that the EoS parameter, skewness parameters in the model turn out to be functions of cosmic time. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-II Dark Energy Model in Scale Covariant Theory of Gravitation

Spatially Homogeneous and anisotropic Bianchi type-II space time with variable equation of state (EoS) parameter and constant deceleration parameter has been investigated in scale covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

Anisotropic Dark Energy Bianchi Type-II Cosmological Models in Lyra Geometry

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological model has been discussed in general relativity in the presence of a hypothetical anisotropic dark energy fluid with constant deceleration parameter within the frame work of Lyra’s manifold with uniform and time varying displacement field vector. With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.     

Higher Dimensional Cosmological Models Filled with Perfect Fluid in f(R,T) Theory of Gravity

The new class of higher dimensional cosmological model of the early universe filled with perfect fluid source in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84, 024020, 2011) is considered. A cosmological model with an appropriate choice of the function f(T) has been constructed. The physical behavior of the model is studied. The well known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with redshift are discussed.     

Kantowski-Sachs Universe Filled with Perfect Fluid in f(R,T) Theory of Gravity

The exact solutions of the field equations in respect of Kantowski-Sachs universe filled with perfect fluid in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84:024020, 2011) is derived. A cosmological model with an appropriate choice of the function f(T) is constructed. The physical behavior of the cosmological model is studied. Some important features of astrophysical phenomena, like Hubble’s parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with red-shift are also discussed.     

Bianchi type-II String Cosmological Model with Magnetic Field in Scale-Covariant Theory of Gravitation

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scale-covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39, 429, 1977). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento 74, 182, 1983) string cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

Bianchi Type-V Cosmology in f(R,T) Gravity with Λ(T)

A new class of cosmological models in f(R,T) modified theories of gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011), where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar R and the trace of the stress-energy tensor T, have been investigated for a specific choice of f(R,T)=f ₁(R)+f ₂(T) by considering time dependent deceleration parameter. The concept of time dependent deceleration parameter (DP) with some proper assumptions yield the average scale factor $a(t) = \sinh^{\frac{1}{n}}(\alpha t)$ , where n and α are positive constants. For 0<n≤1, this generates a class of accelerating models while for n>1, the models of universe exhibit phase transition from early decelerating phase to present accelerating phase which is in good agreement with the results from recent astrophysical observations. Our intention is to reconstruct f(R,T) models inspired by this special law for the deceleration parameter in connection with the theories of modified gravity. In the present study we consider the cosmological constant Λ as a function of the trace of the stress energy-momentum-tensor, and dub such a model “Λ(T) gravity” where we have specified a certain form of Λ(T). Such models may display better uniformity with the cosmological observations. The statefinder diagnostic pair {r,s} parameter has been embraced to characterize different phases of the universe. We also discuss the physical consequences of the derived models.     

Universe Filled with Dark Energy (DE) from a Wet Dark Fluid (WDF) in f(R,T) Gravity

We studied the Bianchi type-V universe filled with dark energy (DE) from a wet dark fluid (WDF) in the framework of f(R,T) gravity (Harko in Phys. Rev. D 84:024020, 2011). A new equation of state for the dark energy (DE) component of the universe has been used. It is modeled on the equation of state p=w(ρ?ρ ^?) which can be describing a liquid, for example water. The exact solutions to the corresponding field equations are obtained for exponential and power-law volumetric expansion. It is observed that the universe can approach to isotropy monotonically even in the presence of wet dark fluid. Also we have discussed the well-known astrophysical phenomena, namely the look-back time, proper distance, the luminosity distance and angular diameter distance with redshift.     

Two Fluid Scenario for Dark Energy Model in a Scalar-Tensor Theory of Gravitation

In this paper, we investigate the evolution of dark energy parameter in the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy in the framework of scalar-tensor theory of gravitation formulated by Saez and Ballester (Phys. Lett. A 113:467, 1986). To obtain a determinate solution special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento B 74:183, 1983) is used. We consider the two cases of interacting and non-interacting fluid (barotropic and dark energy) scenario and obtained general results. The physical aspects of the results obtained are also discussed.     

Bianchi type-I cosmology in f(R,T) gravity

We investigate the exact solutions of a Bianchi type-I space-time in the context of f(R, T) gravity [1], where f(R, T) is an arbitrary function of the Ricci scalar R and the trace of the energy-momentum tensor T. For this purpose, we find two exact solutions using the assumption of a constant deceleration parameter and the variation law of the Hubble parameter. The obtained solutions correspond to two different models of the Universe. The physical behavior of these models is also discussed.     

LRS Bianchi Type II Massive String Cosmological Model for Stiff Fluid Distribution with Decaying Vacuum Energy (Λ)

An LRS Bianchi Type II model formed by massive strings with decaying vacuum energy (Λ) for stiff fluid distribution is studied in the context of general relativity. To get the deterministic model, we have assumed that $\frac{\sigma}{\theta} =\mathrm{constant}$ where σ is shear and θ the expansion in the model and decaying vacuum energy (Λ) is proportional to H ² (H is Hubble parameter) as used in Arbab (Gen. Relativ. Gravit. 29:51, 1997). We find that the model represents decelerating and accelerating phases of universe. The decaying vacuum energy (Λ) is proportional to $\frac{1}{\tau^{2}}$ as obtained by Bertolami (Nuovo Cimento B 93:36, 1986) and Hubble parameter is proportional to $\frac{1}{\tau}$ which matches with the observation. The model in general represents anisotropic space-time. However, in special case, it isotropizes. The particle density (ρ _p ) and string tenson (λ) are initially large but decrease due to lapse of time. The model also admits particle horizon and entropy is inversely proportional absolute temperature. Thus the model is in good agreement with present age of universe.     

Kinematical Implications of a New f(R) Theory of Gravity: The Redshift

In this paper, we discuss the kinematical concepts of a recently defined f(R) action (Payandeh and Fathi in Int. J. Theor. Phys., 2013, doi:10.1007/s10773-013-1770-5). Firstly, we retreat the action to obtain the kinematic representation of the standard cosmology components, and then, we go through our model, to find the cosmological redshift, according to the scalar field constituents of the theory.     

A Higher Dimensional Cosmological Model in a Scale-Covariant Theory of Gravitation

Kaluza-Klein space-time is considered in the presence of a perfect fluid distribution in the scale-covariant theory of gravitation by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983), a cosmological model in five dimensions with a negative constant deceleration parameter is presented in this theory. Some physical and kinematical properties of the model are also discussed.     

Universe Filled with a Binary Mixture of Perfect Fluid and Dark Energy

We consider a self consistent system of Bianchi type-V gravitational field and a binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p=γρ, with γ∈[0,1] whereas, the dark energy is considered to be either the quintessence like equation of state or Chaplygin gas. The equation of state parameter for dark energy ω is found to be consistent with the recent observations of SNe I_a data (Knop et al., Astrophys. J. 598:102, 2003), SNe I_a data with CMBR anisotropy and galaxy clustering statistics (Tegmark et al., Astrophys. J. 606:702, 2004) and latest a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type I_a supernovae and galaxy clustering (Hinshaw et al., Astrophys. J. Suppl. 180:225, 2009; Komatsu et al., Astrophys. J. Suppl. Ser. 180:330, 2009). The physical and geometrical aspects of the models are also discussed in detail.     

A Note on Plane Symmetric Solutions in f(R) Gravity

The static plane symmetric vacuum solutions (Sharif and Shamir in Mod. Phys. Lett. A 25:1281, 2010) for n+1 dimension are reported. For this purpose, the generalized field equations are solved using the assumption of constant scalar curvature in metric f(R) gravity.     

Axially Symmetric Space-Time with Strange Quark Matter Attached to String Cloud in Self Creation Theory and General Relativity

The Axially symmetric space times with strange quark matter attached to string cloud in Barber’s (Gen. Relativ. Gravit. 14, 117, 1982) self-creation theory and general relativity have been studied. The field equations of the two theories have been solved by using the anisotropy feature of the universe in the axially symmetric space times. Some important features of the models, thus obtained, have been discussed and it is established that the additional condition, special law of variation of Hubble parameter proposed by Bermann (Nuovo Cimento B 74, 182, 1983), taken by Katore and Shaikh (Int. J. Teor. Phys. 51, 1881, 2012) in general relativity is superfluous.     

Late-time cosmological approach in mimetic <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

In this paper, we investigate the late-time cosmic acceleration in mimetic f(R, T) gravity with the Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations the main equation that can describe the cosmological evolution. Then, with several models from \(\mathcal {Q}(z)\) and the well-known particular model f(R, T), we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and in each case we compare the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic f(R, T) gravity. The results obtained are in good agreement with the observational data and show that in the presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped.     

Pilgrim dark energy in f(T) gravity

We discuss the interacting f(T) gravity with pressureless matter in an FRW spacetime. We construct an f(T) model by following the correspondence scheme incorporating a recently developed pilgrim dark energy model and taking the Hubble horizon as the IR cutoff. We use constructed model to discuss the evolution trajectories of the equation-of-state parameter, the ω _T -ω′ _T phase plane, and state-finder parameters in the evolving universe. It is found that the equation-of-state parameter gives a phantom era of the accelerated universe for some particular range of the pilgrim parameter. The ω _T -ω′ _T plane represents freezing regions only for an interacting framework, while the ΛCDM limit is attained in the state-finder plane. We also investigate the first and second laws of thermodynamics assuming equal temperatures at and inside the horizon in this scenario. Due to the violation of the first law of thermodynamics in f(T) gravity, we explore the behavior of the entropy production term. The validity of a generalized second law of thermodynamics depends on the present-day value of the Hubble parameter.     

Approximate Lifshitz Law for the Zero-Temperature Stochastic Ising Model in any Dimension

We study the Glauber dynamics for the zero-temperature stochastic Ising model in dimension d ≥ 4 with “plus” boundary condition. Let ${\mathcal{T}_+}$ be the time needed for an hypercube of size L entirely filled with “minus” spins to become entirely “plus”. We prove that ${\mathcal{T}_+}$ is O(L ²(log L) ^c ) for some constant c, not depending on the dimension. This brings further rigorous justification for the so-called “Lifshitz law” ${\mathcal{T}_{+} = O(L^{2})}$ (Fischer and Huse in Phys Rev B 35:6841–6848, 1987; Lifshitz in Sov Phys JETP 15:939–942, 1962) conjectured on heuristic grounds. The key point of our proof is to use the detailed knowledge that we have on the three-dimensional problem: results for fluctuation of monotone interfaces at equilibrium and mixing time for monotone interfaces dynamics extracted from Caputo et al. (Comm Pure Appl Math 64:778–831, 2011) to get the result in higher dimension.